White background turning grey during video creation
Short answer:

Your source and your output need proper color management. 

Long answer:

If your sources have already been mapped to display referred values, then set the input values to sRGB and set the color management to use sRGB as well and set the view to default.



It makes no sense to use filmic blender color transforms if you are not using scene referred values with a wide dynamic range, or if your sources are not log encoded. 

As a side note: if you end up using log encoding, avoid an 8bit format for the images, it will only give you headaches and lots of quantization errors.
Please read this post: https://blender.stackexchange.com/a/46940/1853 to understand how values are mapped.